Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction
Selcted papers from a meeting on Waves and pattern in chemical and biological media
Convergence of finite volume schemes for Poisson's equation on nonuniform meshes
SIAM Journal on Numerical Analysis
Optimal multilevel iterative methods for adaptive grids
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Three-dimensional dissipative structures in reaction-diffusion systems
Proceedings of a NATO advanced research workshop on New trends in nonlinear dynamics : nonvariational aspects: nonvariational aspects
The node-centred finite volume approach: bridge between finite differences and finite elements
Computer Methods in Applied Mechanics and Engineering
Discretisation procedures for multi-physics phenomena
Journal of Computational and Applied Mathematics - Special issue on applied and computational topics in partial differential equations
Algorithmic Beauty of Sea Shells
Algorithmic Beauty of Sea Shells
The Korean Journal of Computational & Applied Mathematics
A moving grid finite element method applied to a model biological pattern generator
Journal of Computational Physics
Journal of Scientific Computing
Mathematics and Computers in Simulation
An unstructured finite volume approach for structural dynamics in response to fluid motions
Computers and Structures
Mathematics and Computers in Simulation
Computers in Biology and Medicine
Journal of Scientific Computing
A finite volume spectral element method for solving magnetohydrodynamic (MHD) equations
Applied Numerical Mathematics
Multiscale analysis for diffusion-driven neutrally stable states
Mathematical and Computer Modelling: An International Journal
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It is well known that reaction-diffusion systems describing Turing models can display very rich pattern formation behavior. Turing systems have been proposed for pattern formation in various biological systems, e.g. patterns in fish, butterflies, lady bugs and etc. A Turing model expresses temporal behavior of the concentrations of two reacting and diffusing chemicals which is represented by coupled reaction-diffusion equations. Since the base of these reaction-diffusion equations arises from the conservation laws, we develop a hybrid finite volume spectral element method for the numerical solution of them and apply the proposed method to Turing system generated by the Schnakenberg model. Also, as numerical simulations, we study the variety of spatio-temporal patterns for various values of diffusion rates in the problem.